It is urgently necessary to establish the small-lot production system of a wide variety of products due to diversification of kinds and short life of the high-technology device products such as semiconductor elements, magnetic storage devices, liquid crystal devices, plasma displays and printed boards. In the manufacture at the core of the production of the high-technology device products, the work of applying photosensitive substance on a material such as wafer and glass substrate and printing out an electric circuit pattern drawn on a mask using an exposure device thereon to form a circuit pattern is repeated. In order to repeatedly form the circuit pattern, the production system takes the job shop type in which the production system includes several hundreds or more of processes and one device has a plurality of processes under its charge, each one of which is composed of a plurality of devices having the same function. Moreover, malfunctioning of one device influences the process quality in proportion to the number of lamination layers of the circuit pattern and accordingly the yield rate of products is influenced truly.
In order to establish the small-lot production system of a wide variety of products by means of such a large-scale and variable job shop type production system, it is indispensable to form the structure of continuous productivity improving activity for early specifying root cause of impeding the productivity of the production system such as quality variation of material, worker's mistake and reduction in productive capacity of device and rapidly taking measures to solve a problem.
Specifically, with regard to reduction in productive capacity of device, there is a problem that the productive capacity is changed due to Production that one machine works for multiple process and High product mix and low product volume production in addition to sudden event such as failure. For example, when the fabrication time in process P for kind A of device X is 1 hour and the fabrication time in process Q for the same kind A of the same device X is 2 hours, the productive capacities of device X for processes P and Q are 1 piece/hour and 0.5 piece/hour, respectively, which are different when the productive capacity is the production number per unit time. Furthermore, when the fabrication time for kind A of device X is 1 hour and the fabrication time for kind B of device X is 2 hours, the productive capacities of device X for kinds A and B are 1 piece/hour and 0.5 piece/hour, respectively, which are different. When the quantity of work in process (WIP) is unexpectedly changed due to cause such as variation in the yield rate, there arise (1) problem that the productive capacity of device is changed due to the multiple-process possession production and (2) problem that the productive capacity of device is changed due to High product mix and low product volume production. As described above, in the job shop type production system and the small-lot production system of a wide variety products, the problems (1) and (2) cause unexpected reduction (bottleneck) of the productive capacity of device and become productivity improvement impeding factor of the production system.
With regard to improvement of the productivity in the production system, as prior-art examples about the method of specifying the device in which the productive capacity is reduced due to the above problems (1) and (2), the following may be referred to.
Patent document 1 proposes a distribution neck diagnosis method for the job shop type manufacturing line for the purpose of estimating a bottleneck state in the production system quantitatively and specifying changing bottleneck process. This method comprises calculating a coefficient of correlation of production quantity (throughput) per unit time of each device in job shop and throughput of the whole production system and graphically representing the correlation coefficients for each device to be compared, so that a device in the bottleneck state is specified.
Patent document 2 proposes a method of monitoring throughput of a production system and its variation in real time and judging whether throughput of device is neither too much nor too little in contradistinction to the throughput of the whole production system and whether variation of the throughput is large or not. The device having problem is regarded as a bottleneck device and when there is a problem, WIP supplied to the device is limited.
Non-patent document 1 proposes a method of classifying the degree of production fluctuation for one device on the basis of analyzed arrival frequency in the queuing theory. The device classified as having large production fluctuation is defined as a bottleneck device having the productive capacity being lacking.
The CV (coefficient of variation) analysis method that is the statistical analysis method proposed in the non-patent document 1 quantifies the performance variation of one device in the production system such as change of throughput and WIP using a coefficient C. The coefficient C is calculated by dividing the standard deviation s by an average value r.C=s/r  expression 1
The coefficient C is used to classify the production fluctuation into three states including a state LV (low variability) having negligibly small variation, a state MV (moderate variability) that variation is apt to be produced and a state HV (high variability) that variation is always produced.    Patent document 1: JP-A-2004-13825    Patent document 2: JP-A-2004-503837    Non-patent document 1: Wallance. J. Hopp, Mark. L. Spreaman, Variability Basics, Factory Physics, p 248-286, Irwin Professional Pub, 1995    Non-patent document 2: Youichi Nonaka, Attila Lengyel, Kouichi Sugimoto, Monitoring Variance in Manufacturing System Performance, 40th CIRP International Seminar on Manufacturing Systems, 2007